A Direct Numerical Approach to Perspective Shape-from-Shading

We introduce a novel numerical method for a recently developed perspective Shape-from-Shading model. In order to discretise the corresponding partial differential equation (PDE), Prados et al. employed the dynamical programming principle yielding a Hamilton-Jacobi-Bellman equation. We reduce that model to its essential, namely to the underlying Hamilton-Jacobi equation. For this PDE, we propose an efficient semi-implicit implementation. Numerical experiments show the usefulness of our approach: Besides reasonable computational times, the method is robust with respect to noise as well as to the choice of the numerical initial condition which is a delicate point for many SFS algorithms.

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